Equations & Inequalities - Unit Test A

1. Solve.

(a)  

3. Solve.

(a)  

If x = -1, then which of the following equations makes a true statement?

• A. 4x + 9 = 20

• B. -4x – 5 = -15

• C. -3x + 15 = 18

• D. -5x – 15 = -22

Answer explanation

The question asks for the equation that is true when x equals -1. Substituting x with -1 in the given options, only the equation -3x + 15 = 18 holds true. Therefore, the correct answer is -3x + 15 = 18.

9. Solve.

(a)  

An air conditioning repair services charges $85.00 per hour, plus a diagnosis fee of $75.00. If the repair costs a total of $385.00, which of the following equations best represents the situation?

• A. 75x + 85 = 385

• B. 85x + 75 = 385

• C. 85x – 75 = 385

• D. 75x – 85 = 385

Answer explanation

The question states that the air conditioning repair service charges $85.00 per hour plus a diagnosis fee of $75.00. The total cost of the repair is $385.00. The equation that best represents this situation is '85x + 75 = 385'. Here, 'x' represents the number of hours of repair service. The cost per hour is multiplied by the number of hours, and the diagnosis fee is added to get the total cost.

Which number line best represents the solution to the problem below?

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Solve.

(a)  

Identify the equation modeled below, and then find its solution.

• A. Equation: 2x + 3 = 8; Solution: x = 5

• B. Equation: 2x – 3 = 8 ; Solution: x = 5.5

• C. Equation: 2x + 3 = 8; Solution: x = 2.5

• D. Equation: x + 3 = 8; Solution: x = 5

Answer explanation

The question asks to identify the equation and find its solution. The correct answer is 'Equation: 2x + 3 = 8; Solution: x = 2.5'. This is because when you solve the equation 2x + 3 = 8, you subtract 3 from both sides to get 2x = 5, and then divide by 2 to find that x = 2.5.

A fifteen passenger van is rented for a family vacation. The van rental is $75.00 per day, plus a $160.00 insurance fee. Which inequality could be used to find x, the number of days the van can be rented if they want to spend less than $760.00 on the van rental?

• A. 75.00 + 160.00x < 760.00

• B. 75.00x + 160.00 > 760.00

• C. 75.00 + 160.00x > 760.00

• D. 75.00x + 160.00 < 760.00

Answer explanation

The question asks for the number of days the van can be rented for less than $760. The cost of the van rental per day is $75 and there is a one-time insurance fee of $160. Therefore, the total cost for x days would be 75x (the daily rental fee) plus 160 (the insurance fee). This total cost must be less than $760, which is represented by the inequality 75x + 160 < 760.

Solve.

(a)